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Fourth International Symposium on Marine Propulsors
smp’15, Austin, Texas, USA, June 2015
Influence of the Numerical Propulsion Modelling on the Velocity
Distribution behind the Propulsion Device and Manoeuvring Forces
*Jan Clemens Neitzel1, Markus Pergande1, Stephan Berger1, Moustafa Abdel-Maksoud1
1Institute for Fluid Dynamics and Ship Theory, Hamburg University of Technology (TUHH), Hamburg, Germany
*Corresponding author: [email protected]
Abstract
The influence of different propulsor modelling
approaches on manoeuvring simulations and rudder
forces is analysed. In the numerical study, the RANS
solver ANSYS CFX is employed. Three approaches for
modelling the propulsor are investigated: a fully
modelled propeller, a coupled simulation with a
potential flow solver and an actuator disk. For the
validation, open water and captive model test results
are used.
1 Introduction
The numerical investigation of ship manoeuvres with
RANS methods often causes a huge computational
effort. In order to accurately capture relevant effects as
for example propeller and rudder forces or the
influence of the free water surface, a relatively fine
discretisation with respect to space and time is
required. A considerable percentage of the
computational effort is due to modelling the propeller
in a geometrically resolved manner.
Therefore, the development of different modelling
techniques to consider the influence of the propulsion
unit on the flow is required for time-efficient
simulations. In RANS simulations, the propeller can be
included as a fully modelled propeller or by applying
the body-force technique. The calculation of the body
force distribution can be based on coupling with a
boundary element method or using an actuator disk
model.
The fully resolved propeller is a common method to
simulate the propulsor either in open water condition
or behind a ship hull. Greve et al. (2010) contributed a
study on the general forces acting on the ship under
propulsion test condition. Bugalski et al. (2011)
demonstrate a good accordance of the experimental
and numerical results for the MOERI KCS container
ship. A detailed study of the effects of the fully
modelled propeller on the flow behaviour behind the
propulsor is done by Krasilnikov (2013).
Coupling a viscous method for the outer flow with an
inviscid boundary element method (BEM) permits the
consideration of the local forces generated by the
blades as shown by Wöckner et al (2011). Rijpkema et
al. (2013) examined the behaviour of the propulsor
behind a ship hull with a RANS-BEM. The application
of the BEM coupling algorithm displays a slight error
of 2 to 3% in comparison to experimental data.
Krasilnikov (2013) furthermore investigated the
influence of an actuator disk for the simulation of the
propeller. Concluding on a good agreement, the
advantage of a significantly lower amount of
computational effort is emphasized. With regard to
work done by Soukup (2008) and Xing-Kaeding
(2006) the actuator disk model can be seen as a
reasonable alternative for propulsor modelling.
The following paper focuses on the interaction of
propeller, hull and rudder for the three mentioned
modelling techniques. The applicability of the
numerical fluid dynamics calculations is investigated
and the results of the simulations are compared to
model test results. Therefore, the forces acting on the
propeller, hull and rudder are calculated and the
velocity distribution behind the propeller is analysed.
2 Propulsor modelling
2.1 Boundary element method
coupling
The RANS-BEM coupling for ANSYS CFX was
implemented by Berger (2013). The coupling
procedure uses the in-house potential code panMARE
developed at the Institute for Fluid Dynamics and Ship
Theory at the Hamburg University of Technology.
panMARE is a first-order potential flow solver. It is
assumed that the total velocity U in the flow domain Ω
can be divided in a background velocity field U∞ and
an induced flow field U+. The total velocity in the
global coordinate system can thus be written as:
𝑼 = 𝑼∞ + 𝑼+ [1]
In a body-fixed coordinate system rotating with the
propeller, Equation [1] is rewritten to:
𝑽 = 𝑽𝒎𝒐𝒕 + 𝑽∞ + 𝑽+ [2]
Vmot is the velocity due to the local body motion and
the background flow is considered as V∞. The induced
flow field V+ is assumed to be incompressible and
irrotational. Hence, a velocity potential Φ = Φ(X,t)
with V+ = ∇Φ can be introduced. Φ is a function of
position and time. The governing flow equations can
be simplified to Laplace’s equation for the potential Φ
and Bernoulli’s equation for the pressure p:
∇2𝚽 = 0 [3]
and
𝑝 +1
2𝜌|𝑽|2 + 𝜌
𝜕𝚽
𝜕𝑡+ 𝜌𝑔𝑧
= 𝑝𝑟𝑒𝑓
+1
2𝜌|𝑽𝟎|2
[4]
with the reference pressure pref. For a lifting body like
a propeller, the surface 𝑆 = 𝜕𝛀 is divided into the
blade surface SB and a part on the wake surface SW. It
is representing the trailing wake propagating from the
trailing edge of the body and the surface S∞ at infinity.
For an arbitrary point 𝑿0ϵ 𝛀 the potential Φ resulting
from a distribution of sources 𝜎 = 𝜎(𝑿) and dipoles
𝜇 = 𝜇(𝑿) on SB and dipoles on SW can be obtained by
Green’s third identity:
𝚽(𝐗0) =1
4𝜋∫ 𝜇∇ (
1
𝑑) 𝒏𝑑𝑆
𝑆𝐵∪𝑆𝑊
− 1
4𝜋∫
𝜎
𝑑𝑑𝑆
𝑆𝐵
[5]
where 𝒏 = 𝒏(𝑿) is the normal vector of the surface
element 𝑑𝑆 and 𝑑 = ‖𝑿 − 𝑿0‖. For 𝑿𝜖𝑆𝐵 ∪ 𝑆𝑊 holds
𝜎 = −∇𝚽 ∙ 𝒏 and 𝜇 = −𝚽. [6]
In order to obtain a physically meaningful potential
and velocity field, boundary conditions have to be
fulfilled on SB, SW and S∞.
Fulfilling the physical Kutta condition on the wake
boundary SW in a direct way requires an iterative
solution procedure. In order to simplify the
calculations, Morino’s Kutta condition (Morino &
Kuo, 1974) is applied:
𝜇𝑊 = 𝜇𝑢 − 𝜇𝑙 [7]
It is based on the relation between the dipole strengths
of the upper and lower side of the trailing edge and the
dipole strengths of the wake surface directly behind the
trailing edge.
Equation [5], combined with the above boundary
conditions, results in a boundary value problem that is
solved by the panel method. Hereby, the surfaces SB
and SW are discretised by quadrilateral elements and
the boundary conditions are applied at the collocation
points X0 of each panel element. Dipoles and sources
are assumed to be constant over one panel. The wake
surface SW is aligned along the streamlines of the
velocity field V in an iterative manner in order to
account for the wake roll-up. The discretised problem
results in a set of linear equations for the unknown
source and dipole strength, which can be solved
numerically by the Gauss method.
In order to carry out a coupled simulation, the
geometrically resolved propeller in the RANS
simulation is replaced by a corresponding distribution
of body forces. Therefore, it is necessary to map the
force distribution on the blades obtained by the panel
method to the volume mesh used by the RANS solver.
The involved algorithm is explained in (Berger, et al.,
2013). For the simulation of the propeller flow in
panMARE, the effective wake field is used as
background flow U∞. The effective wake field is
approximated by subtracting the propeller-induced
velocities from the total velocity field in front of the
propeller which is calculated by the RANS solver.
2.2 Actuator disk
The actuator disk model is based on the approach of
Manzke (2008) that refers to the numerical studies of
Soukup (2008) and Xing-Kaeding (2006). The velocity
distribution is taken from the current RANS solution at
an axial distance of 0.05D in front of the leading edge,
where D is the propeller diameter. As a modification,
the local thrust for each cell volume is calculated based
on the momentum theory. The modification takes the
influences of the local inflow into account.
For each cell volume, the body force is set iteratively.
With the inflow velocity vp,local, a first guess of the
thrust Tp,local is derived. The local advance coefficient
Jlocal for each control volume can be written as
𝐽𝑙𝑜𝑐𝑎𝑙 = 𝑣𝐴,𝑙𝑜𝑐𝑎𝑙
𝑛𝐷 ± 𝑣𝑇,𝑙𝑜𝑐𝑎𝑙
𝜋
[8]
with the advance velocity vA,local far in front of the
propeller, the tangential velocity vT,local and the number
of revolutions n, which is fixed during the iteration.
The change of tangential velocity in front of the
propeller is neglected, therefore vT,local at the inflow
plane (0.05D) is taken. The consideration of the
tangential velocity is necessary to take into account the
influence of the oblique inflow at the propeller
location. Including data of the corresponding thrust
coefficient kT from the open water diagram according
to the estimated J-value and the propeller diameter D,
the initial solution is valid for the inflow velocity vp,local
being equal to the advance velocity vA,local.
𝑇𝑝,𝑙𝑜𝑐𝑎𝑙 = 𝑘𝑇
𝐽𝑙𝑜𝑐𝑎𝑙2 𝜌𝐷2𝑣𝐴,𝑙𝑜𝑐𝑎𝑙
2 [9]
As it can be shown by momentum theory, a relation of
the advance velocity to the local propeller inflow
velocity can be deducted.
𝑣𝐴,𝑙𝑜𝑐𝑎𝑙 = 2𝑣𝑝,𝑙𝑜𝑐𝑎𝑙
1 + √1 +8𝜋
𝑘𝑇
𝐽𝑙𝑜𝑐𝑎𝑙2
[10]
The advance velocity vA,local far in front of the propeller
depends on the inflow velocity vp,local and a value for
the advance coefficient Jlocal, see Equation [10]. As
shown in Equation [8], the advance velocity vA,local is
part of the advance coefficient. Hence, an iterative
solution procedure is necessary to choose the correct
thrust and torque for each cell according to the local
inflow.
𝑇𝑙𝑜𝑐𝑎𝑙 = 𝑘𝑇𝜌𝑛2𝐷4 [11]
𝑄𝑙𝑜𝑐𝑎𝑙 = 𝑘𝑄𝜌𝑛2𝐷5 [12]
A radial distribution r´ according to Equation [13] is
introduced.
𝑟´ = 𝑟 − 𝑟ℎ
𝑟𝑝 − 𝑟ℎ√1 −
𝑟 − 𝑟ℎ
𝑟𝑝 − 𝑟ℎ
[13]
, where rp and rh are the propeller radius and the hub
radius, respectively. The distribution is similar to the
radial thrust distribution of a real propeller with its
maximum near 0.7R. Near the blade tip and the
propeller hub (rh) the value of r´ is zero.
On basis of the local thrust and torque values (see Eq.
[11] and [12]) multiplied with the distribution function
r´, the body forces for each cell volume can be applied.
After integration of the local thrust values over the
propeller disk, a correction factor is needed to meet the
total thrust.
2.3 Fully modelled propeller
Instead of representing the propulsor by using body
forces, the flow around the propeller blades and the
hub can be simulated directly with a RANS solver. The
surface of the propeller is therefore discretized with
triangular prism cells. A volume mesh is created
around the propulsor with a refinement related to the
local curvature of the blade surface. With increasing
distance to the surface the mesh refinement is reduced.
Obtaining the corresponding rotation rate and an
inflow condition, the fluid forces on the propeller and
the influence on the flow behaviour can be calculated
directly in RANS simulations.
3 Case study
3.1 Geometry
The ship investigated numerically in this paper is a
feeder container vessel. Initially designed within a
research project at the Potsdam Ship Model Basin, the
feeder ship is not built in full scale. Table 1 shows the
main ship data. The hull is investigated in model scale
and the applied scale factor is 19.2.
Table 1: Main ship data of the Feeder ship
Full Scale Model Scale
Lpp 110.0 m 5.73 m
Lwl 112.5 m 5.86 m
Bwl 18.0 m 0.94 m
T 7.1 m 0.37 m
VDesign 14.0 kn 1.64 m/s
V1 10.0 kn 1.17 m/s
The ship is driven by a four-bladed controllable pitch
propeller with a diameter of 4.6 m. Table 2 contains the
main propeller data.
Table 2: Main propeller data in design condition
Full Scale Model Scale
D 4.6 m 0.24 m
Z 4 4
P/D0.7R 0.8 0.8
Hub ratio 0.188 0.188
The model propeller has a diameter of 0.24 m. The
pitch-diameter ratio at 0.7R is 0.8, where R is the
propeller radius. The propeller rotates clockwise
around the x-axis, viewed from astern. The x-axis is
directed towards the bow of the ship and is located
along the symmetry plane.
3.2 Model tests
The following numerical simulations have been carried
out:
Hull resistance test:
The ship hull with the rudder is towed in calm water at
constant ship speed.
Propeller open water test:
The open water test is carried out in the towing tank,
measurements are carried out at different numbers of
revolutions.
Captive propulsion test
The ship model is towed several times with a constant
speed in calm water. Each time the propeller operates
with a fixed rotation rate. The forces acting on the ship,
the rudder and the propeller are measured separately.
This corresponds to the British propulsion model test
method.
Planar Motion Mechanism – Surge:
In this test, the ship model is connected to a planar
motion mechanism, which is fixed to a towing
carriage. While the towing carriage moves ahead with
a constant speed, the planar motion mechanism forces
the ship model to perform a sinusoidal surge motion.
The rudder angle and the course angle of the ship are
kept zero during the test. The propeller operates with a
fixed rotation rate. The results include the forces acting
on the ship, the rudder and the propeller.
The sinusoidal surge motion has the amplitude A. With
respect to the desired maximum surge motion
amplitude and the period of the surge motion, the time-
dependent surge velocity can be determined, see
Equation [14].
�̇�(𝑡) = 𝐴𝜔 cos(𝜔𝑡) [14]
4 Numerical setup
4.1 General setup
The numerical calculations are performed using the
flow solver ANSYS CFX. In order to represent
turbulence in the near-wall and free stream region, the
Shear Stress Transport model (SST) (Menter, 1992) is
used. The free surface interface is modelled by the
volume of fluid method (VOF) (Nichols & C.W,
1981).
All simulation are carried out with a fixed floating
position with zero trim corresponding to the design
waterline.
4.2 Ship Domain
The purpose of the numerical simulation of the ship
flow is the calculation of the forces acting on the hull,
the appendages and the propulsion device. The flow
around the ship model during the captive surge motion
shows a strong influence of the free surface on the
estimated hull forces. Therefore, in the computations
an accurate capturing of the free surface is essential to
achieve a reliable estimation of hull forces.
Additionally, in the numerical simulation a detailed
view is given on the propulsion device and its
interaction with the rudder and the hull. A fine mesh
near the mentioned parts of the ship is required.
Figure 1: Topology of the computation domain
Figure 1 shows the computation domain including the
ship and a subdomain to perform mesh motions, where
the box around the ship moves.
Figure 2: Aft ship with rudder and cylindrical box for
the propulsor
The mesh consists of 5.4 million cells. The underwater
hull surface is discretised with 26,000 surface cells, the
rudder surface has 10,000 surface cells (see Figure 2).
The near-wall sub-layer consists of 12 rows of prism
cells with a growth ratio of 1.1. The near-wall cell
height is adapted to achieve a local non-dimensional
wall distance of y+=30.
4.3 Propeller Domain
The mesh of the fully modelled propeller consists of
2.43 million cells. Each blade is discretised with
25,000 surface cells. 12 prismatic cell layers with a
growth ratio of 1.1 represent the viscous sublayer. The
propeller is located in a cylindrical domain, which
rotates around the center axis of the shaft (see Figure
3).
Figure 3: Mesh around the propeller and the ship
stern
The domain for modelling the virtual propeller based
on body forces includes 250,000 control volumes. In
this domain the propeller hub is also considered. The
dimensions of the cylindrical domain are similar to the
fully modelled propeller domain.
5 Results
5.1 Resistance
The resistance of the ship is evaluated for the design
speed VDesing = 14 kn and for another speed V1=10 kn.
The resistance data can be seen in Table 3.
Table 3: Resistance data for the Feeder ship
V [kn] Model test [N] Calculation [N]
VDesign 14 45.65 45.38
V1 10 24.96 24.42
The deviation of the calculated resistance force for a
full scale velocity of 14 kn is 0.59 % of the model test
result. For V1 the deviation is slightly larger.
5.2 Propeller open water test
The results of the propeller open water test allow a
conclusion on the accuracy of forces calculated with
the different propeller modelling techniques. In Figure
4, the thrust coefficient is plotted over the advance
coefficient. The thrust of the fully modelled propeller
(FMP) is in very good agreement with the model test
results (EFD). For the range of the advance coefficients
considered, the deviation of the value is in a 2%-range
of the EFD results.
Figure 4: Thrust coefficient for the propulsion
modelling techniques under open water conditions
The thrust coefficient calculated by the boundary
element method (BEM) depicts a deviation for off-
design advance coefficients, especially for small J-
values. However, the comparison of the results to the
model test results are in good agreement for a range of
the advance coefficient between 0.5 and 0.8, which are
within the main operating range of the propeller behind
the ship.
The actuator disk model (AD) overestimates the thrust
for advance coefficients less than 0.6. This may be
caused by the limitation of the applicability of the
momentum theory to render the induced velocities near
the propeller disc (see Equation [10]).
5.3 Captive propulsion test
Captive propulsion tests offer a close insight in the
interaction of the propeller, the hull and the
appendages located in the propeller slipstream. A
variation of the propeller load changes the flow
behaviour in the aft ship region.
The numerical models are conducted to represent the
propeller thrust behaviour and the local influence on
-0,1
-0,05
0
0,05
0,1
0,15
0,2
0,25
0,3
0,35
0,2 0,4 0,6 0,8
k T
J
Thrust coefficient
EFD FMP AD BEM
the fluid velocity distribution around the aft ship hull.
All presented results are averaged over one propeller
revolution.
Table 4: Total force on the ship and propeller thrust
Model
n
[rps]
Fx Total
[N]
Thrust
[N]
Fx Rudder
[N]
EFD
8
-24.62 26.57 -1.39
FMP -24.22 27.53 -1.71
AD -26.36 24.64 -2.34
BEM -23.18 27.27 -2.48
EFD
8.773
-15.29 37.59 -1.60
FMP -15.28 38.43 -1.85
AD -15.60 36.98 -2.62
BEM -14.29 38.14 -2.88
EFD
10
2.71 58.93 -1.85
FMP 2.36 58.84 -2.11
AD 2.44 58.29 -2.65
BEM 2.01 57.36 -3.61
Table 4 includes the propeller thrust and the total
forces in the local x-direction for 3 different rotation
rates and VDesign. The total force includes the ship
resistance, the rudder resistance as well as the propeller
thrust. The results of the fully modelled propeller case
(FMP) are in good agreement with the EFD for the
towing force and the thrust. The actuator disk model
(AD) underestimates the thrust. It leads to a slightly
lower thrust and therefore a larger towing force.
For higher rotation rates of 8.773 rps and 10 rps the
modelling techniques FMP and AD lead to results that
are very close to the EFD results. For the rotation rate
of 10 rps, the propeller thrust is higher than the
resistance of the ship and the rudder, which leads to a
positive total force.
Furthermore, Table 4 shows the forces on the rudder in
the x-direction. For all evaluated operating conditions,
the resistance force of the rudder is overestimated in
the numerical simulations. The usage of the FMP leads
to a less over prediction compared with AD and BEM
coupling.
For further understanding of the influence of the
propulsion modelling on the local flow state behind the
propulsion device, the averaged velocity distribution is
focused now at a location 0.25D downstream of the
propeller center. In Figure 5, the local velocities behind
the propeller are shown.
The maximum axial velocity is 2.21 m/s for the FMP
and 2.35 m/s for the AD, whereas the average velocity
is almost similar for both cases (AD: 1.41 m/s, FMP:
1.45 m/s). The contours of the velocity component in
the y-direction (middle figure) at the 12 o’clock
position are more pronounced in the FMP case. Higher
velocities in the y-direction lead to a higher angle of
attack at the rudder resulting in a lift force. The
increase of the angle of attack leads to a proportional
increase of the lift force. This force acts against the
resistance force. The velocity distribution in z-
direction is mainly quite similar and seems to have no
Figure 5: Averaged velocity distribution in [m/s] 0.25D behind the propeller for the AD case (upper row) and the
FMP case (lower row), rotation rate of 10 rps, ship speed 14 kn in full scale
significant effect on the forces acting on the rudder.
For lower rotation rates the differences in the
distributions are smaller, but they show the same
tendency as presented in Figure 5.
A comparison of the BEM coupling with the FMP case
for a rotation rate of 10 rps is shown in Figure 6. The
velocity distributions are quite similar. The maximum
velocity in axial direction is with a value of 2.32 m/s
higher than the 2.21 m/s in the FMP case. The average
axial velocity behind the propeller is with a value of
1.37 m/s lower than in the FMP case.
A more detailed view on the influence of the propeller
on the flow behaviour can be seen in Figure 7. The
velocity distribution in a distance of 0.25D in front of
the propeller (upstream) is compared to the flow
behaviour 0.25D behind the propeller (downstream)
for the three modelling techniques. The given angle
describes the location of the blade during a rotation of
the propeller. An angle of 0° corresponds to the 12
o’clock position. The values shown in the following
figures are averaged over one revolution of the
propeller.
With a rotation rate of 10 rps at a ship speed of
vDesign=14 kn, the fluid approaches the propeller with
around 90% of the design speed between 60° and 300°.
The reduction of the axial velocity at an angle of 0° is
typical for a wake field of a ship with a single screw.
The propeller accelerates the fluid to a velocity 30%
higher than the ship speed, with a reduction at 0° and
180° due to the influence of the rudder.
Figure 7: Velocity in axial direction in front of and
behind the propeller on 0.7R (10 rps, VDesign)
Caused by a general upward flow upstream of the
propeller, the radial velocity distribution in Figure 8 is
mainly influenced by the vertical velocity, working in
a negative radial direction for blade angles between
90° and 270°. The velocity distribution behind the
propeller indicates a contraction of the slip stream for
the mentioned range of angles, resulting in negative
radial velocities. For blade angles between 300° and
60°, the rudder induces a velocity directed outward,
leading the flow around the rudder. Due to a high thrust
loading in the range between 0° and 60°, a large
deviation between the results of the three applied
methods can be observed downstream of the propeller.
0,2
0,4
0,6
0,8
1,0
1,2
1,4
1,6
0 60 120 180 240 300 360
v x/v
Des
ign
Blade angle [°]
Axial velocity distribution
FPM (downstream) FPM (upstream)BEM (downstream) BEM (upstream)AD (downstream) AD (upstream)
Figure 6: Averaged velocity distribution in [m/s] 0.25D behind the propulsion device for the BEM case (upper row)
and the FMP case (lower row), rotation rate of 10 rps, ship speed 14 kn in full scale
Figure 8: Velocity in radial direction in front of and
behind the propeller on 0.7R (10 rps, VDesign)
The tangential velocity distribution does not indicate
any significant differences, see Figure 9. Thus, the
deviation of the rudder resistance force in Table 4
cannot be explained by different tangential velocities.
The velocity distribution indicates a symmetric inflow
to the propeller. For angles in a range between 60° and
180°, the propeller benefits from the pre-swirl energy.
As a result, the advance coefficient in Equation [8]
decreases, which leads to an increase of the local
thrust.
Due to the contrary direction of the fluid and the
propeller blades, the resulting vertical velocity
downstream of the propeller is zero. For blade angles
larger than 180°, the propeller blades produce a swirl
with the same orientation as the tangential flow
velocity in front of the propeller. The advance
coefficient increases. The pre-swirl and the rotational
loss of the propeller have the same direction of rotation
and results in a large tangential velocity.
Figure 9: Velocity in tangential direction in front of
and behind the propeller on 0.7R (10 rps, VDesign)
In Figure 7 and Figure 9 in a range between 180° and
360°, the AD model overestimates the axial velocity
and tangential velocity components downstream of the
propeller, compared to the FMP and BEM cases. Thus,
the local effect of the tangential velocities on the fluid
acceleration by the propeller is not sufficiently
captured by the AD model.
5.4 Planar Motion Mechanism –
Surge
The capability of the actuator model for dynamic tests
is demonstrated exemplarily for surge motion.
In the planar motion test, the ship is running ahead with
a velocity of 14 kn. Then, the ship is forced to perform
a surge motion as shown in Figure 10. The time 0 s
indicates the start of a surge period. Referring to
Equation [14] the maximum change of the ship’s speed
relative to the fluid velocity is 0.235 m/s
(corresponding to full scale velocity: 2 kn).
-0,4
-0,3
-0,2
-0,1
0,0
0,1
0,2
0,3
0,4
0 60 120 180 240 300 360v R/v
Des
ign
Blade angle [°]
Radial velocity distribution
FPM (downstream) FPM (upstream)BEM (downstream) BEM (upstream)AD (downstream) AD (upstream)
-0,5
-0,3
-0,1
0,1
0,3
0,5
0 60 120 180 240 300 360v T/v
Des
ign
Blade angle [°]
Tangential velocity distribution
FPM (downstream) FPM (upstream)BEM (downstream) BEM (upstream)AD (downstream) AD (upstream)
Figure 10: x-Displacement of the ship under planar
surge motion conditions
The force in x-direction is not symmetric in Figure 11,
because it is shifted by the steady ship resistance
component. The propeller model operates in an
oscillating inflow velocity field and thus causes a
periodical change of the rudder resistance, see Figure
12.
Figure 11: Force in x-direction on the ship hull under
planar surge motion conditions
Figure 12: Force in x-direction on the rudder under
planar surge motion conditions
The maximum rudder force shown in Figure 12 occurs
at around 2.5 s. That instant of time is in accordance
with the maximum value of the thrust in Figure 13.
Figure 13: Propeller thrust under planar surge motion
conditions
6 Conclusion
The captive propulsion test allows the evaluation of the
applicability of the different propulsion modelling
techniques for simulation of ship manoeuvres. The
propeller modelling techniques applied in the paper are
able to capture the propeller forces and the flow
behaviour around the aft-ship and the rudder.
Where, over the investigated range of propeller loading
conditions, the results of the fully modelled propeller
show a good agreement with the measured values. The
results of the actuator disk and the BEM coupling
method are in good agreement with the experimental
results only for advance coefficients close to the design
condition.
For lower propeller loading conditions, the actuator
disk model generates a significantly less thrust than the
measured value. The BEM coupling method is
generally in good agreement with the measured results
and the computation time is much less than the time
required for simulation with a fully modelled propeller.
The application of the actuator disk model for planar
motion surge mechanism simulations delivers realistic
results and much less computation time is required,
compared with the other two simulation techniques.
7 Acknowledgement
The work presented in this paper is part of the tasks to
be executed in the research project “OptiStopp”. The
research project is supported by the Federal Ministry
-0,2
-0,1
0
0,1
0,2
0 2 4 6dX
[m]
Time [s]
x-Displacement of the ship
∆X
-150
-100
-50
0
50
0 2 4 6
F X[N
]
Time [s]
Force in x-direction on the hull
Fx, hull
-4
-3
-2
-1
0
0 2 4 6
F X[N
]
Time [s]
Force in x-direction on the rudder
Fx, rudder
32
34
36
38
40
42
0 2 4 6
T X[N
]
Time [s]
Propeller thrust
Thrust
of Economic Affairs and Energy of Germany. The aim
of the project is to simulate stopping manoeuvres using
time-efficient system based methods. The project
partners are Thyssen Krupp Marine Systems GmbH,
SVA Potsdam GmbH and Siemens AG.
8 References
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Berger, S., Bauer, M., Druckenbrod, M. & Abdel-
Maksoud, M., 2013. An Efficient Viscous/Inviscid
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Soukup, P., 2008. Report on Free Running Model
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Hamburg: Hamburg University of Technology.
9 DISCUSSION
9.1 Question from Sverre Steen
The title of the paper mentions manoeuvring, and
in the introduction part of the presentation you state
that crashback is the ultimate aim of your work, while
what you present here is just straight ahead. How do
you plan to address the complicated, separated flow of
the crashback condition?
9.2 Authors’ Closure
Thank you for your observation. The crashback
situation with the propeller acting opposite to the
general flow direction is indeed a highly complicated
case. Since the general approach using the actuator
disk model based on the momentum theory is not valid
for off-design cases, a specification containing a
prescribed thrust and torque and a distribution factor
for a tangential distribution will be implemented.
Based on a few simulations for flow conditions
occurring during a crashback manoeuvre with a fully-
modelled propeller, the prescribed input values for the
actuator will be interpolated and the coefficients for the
off-design conditions can be calculated.